Preheat oven to 425ºF. Line 2 rimmed baking sheets with parchment.
Divide dough into 10 equal pieces and roll each into a ball. Place balls on a lightly floured countertop and loosely cover with plastic wrap. Let stand until dough is room temperature and easy to shape, 15 minutes to 1 hour.
Place sauce, cheese, pepperoni, olives, mushrooms, artichoke hearts, peppers and broccoli in bowls with spoons or forks. Sprinkle a work surface with flour. Let each party guest press and stretch a ball of dough into a 5-inch circle and top with sauce, cheese, pepperoni and vegetables as desired.
Carefully transfer pizzas to baking sheets. Write each guest's name next to his pizza (don't let pizzas touch ink). Bake 1 sheet at a time until crusts are golden and cheese is bubbling, for 15 to 18 minutes. Let cool on baking sheets for 10 minutes. Repeat with second sheet. Serve.